[1]熊辉,杨光.含凹凸非线性的p(x)-Laplace方程多正解的存在性[J].江西师范大学学报(自然科学版),2014,(03):254-257.
 XIONG Hui,YANG Guang.The Existence of Multiple Positive Solutions for the p(x)-Laplacian Equation with Concave and Convex Nonlinearities[J].,2014,(03):254-257.
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含凹凸非线性的p(x)-Laplace方程多正解的存在性()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年03期
页码:
254-257
栏目:
出版日期:
2014-06-30

文章信息/Info

Title:
The Existence of Multiple Positive Solutions for the p(x)-Laplacian Equation with Concave and Convex Nonlinearities
作者:
熊辉;杨光
东莞理工学院数学教研室,广东 东莞,523808
Author(s):
XIONG Hui;YANG Guang
关键词:
凹凸非线性正解存在性山路原理Ekeland变分原理
Keywords:
concave and convex nonlinearityexistence of positive solutionsmountain pass theoremEkeland varia-tional principle
分类号:
O175.24;O411.3
文献标志码:
A
摘要:
利用基于临界点理论的变分方法和Ekeland变分原理,研究含凹凸非线性的参数型p( x)-Laplace方程的Dirichlet问题的正解的存在性。在该方程中,超线性项不需要满足Ambrosetti-Rabinowitz条件,对于取值较小的参数,证明了所研究的问题至少有2个非平凡的光滑正解。
Abstract:
Using variational methods based on the critical point theory and the Ekeland variational principle,a non-linear parametric Dirichlet problem,driven by the anisotropic p( x)-Laplacian with the combined effects of concave and convex terms,is studied. In this problem,the superlinear nonlinearity does not need to satisfy the Ambrosetti-Rabinowitz condition. It is shown that for small values of the parameter,the problem has at least two nontrivial smooth positive solutions.

参考文献/References:

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备注/Memo

备注/Memo:
国家自然科学基金(11271069)
更新日期/Last Update: 1900-01-01